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arXiv:1302.5826 · Annals of Physics

A remark on the role of indeterminism and non-locality in the violation of Bell’s inequalities

Massimiliano Sassoli de Bianchi

Published Jan 3, 2014• 12 citations
arXivHTMLPDF
DOI
10.1016/j.aop.2013.12.011

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In this paper we would like to stress that, besides two commonly discussed conditions inducing violation of Bell’s inequality—nonlocality and death of realism—there is the third condition having the same consequence. This is the condition of probabilistic incompatibility (PI) of random variables—impossibility to realize them on a single probability space—“non‐Kolmogorovness.” This additional source of violation of Bell’s inequality should be taken into account. We remark that PI can be a consequence of nonlocality or impossibility to use the realistic model. However, PI is essentially more general condition. Random variables can be of the PI‐type even in absence of nonolocal effects.
If the world is not deterministic, then at the very least, some individual events just happen ’by chance’. But the frequency of such events and correlations between them could be subject to constraints, whether local or non‐local. Hans Reichenbach introduced a principle weaker than determinism but non‐trivial: that every positive correlation should be traceable to a common cause (defined in terms of temporal precedence plus certain probabilistic relations). This principle turns out to imply the Bell Inequalities, which quantum theory violates. This chapter discusses the logical relations between indeterminism, common cause models, the Bell Inequalities, non‐contextual hidden variable models, and various concepts of locality and non‐locality, as well as the experiments designed to reveal the predicted violations.
A violation of Bell-CHSH inequalities does not justify speculations about quantum non-locality, conspiracy and retro-causation. Such speculations are rooted in a belief that setting dependence of hidden variables in a probabilistic model (called a violation of measurement independence (MI)) would mean a violation of experimenters’ freedom of choice. This belief is unfounded because it is based on a questionable use of Bayes Theorem and on incorrect causal interpretation of conditional probabilities. In Bell-local realistic model, hidden variables describe only photonic beams created by a source, thus they cannot depend on randomly chosen experimental settings. However, if hidden variables describing measuring instruments are correctly incorporated into a contextual probabilistic model a violation of inequalities and an apparent violation of no-signaling reported in Bell tests can be explained without evoking quantum non-locality. Therefore, for us, a violation of Bell-CHSH inequalities proves only that hidden variables have to depend on settings confirming contextual character of quantum observables and an active role played by measuring instruments. Bell thought that he had to choose between non-locality and the violation of experimenters’ freedom of choice. From two bad choices he chose non-locality. Today he would probably choose the violation of MI understood as contextuality.